Linear integral equation

An integral equation in which the unknown function $\phi(s)$ occurs in a linear fashion:
$$A(x)\phi(x)+\int\limits_DK(x,s)\phi(s)ds=f(x),\quad x\in D.$$
Here $A$, $K$, $f$ are given functions, $D$ is a domain of the Euclidean space, $k$ and $s$ are points of the space, and $ds$ is the volume element. For more details see Integral equation.